Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C25 ⋊ #131 |
93 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=e,c^2=e,d^2=e,f^5=g,f^a=f^2g,g^a=g^2,c^b=ce,f^d=f^4g^4,g^d=g^450 conjugacy classes — view the full character table.
| maximal subgroup of | #13098723, #13098724, #13098727, … |
| maximal normal subgroup of | #13098723, #13098724, #13098727, … |
| maximal quotient of | #13098690, #13098691, #13098692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 211);